In seismic exploration of formations below bodies of water, such as a lake or ocean, in some cases an acoustic source is used to create the interrogating energy. In particular, the acoustic source is suspended in the water at a known depth and the acoustic source is activated at known times. The acoustic wavefield, comprising pressure wavefield and fluid particle velocity wavefield components, propagates through the water, into the formation below the sea floor, and a portion of the acoustic energy therein is reflected and propagates back for detection by sensors deployed in the water body or on the sea floor beneath the water body. (The pressure and fluid particle velocity wavefield components may simply be referred to as pressure and fluid particle velocity wavefields, respectively.) Based on the known activation time of the acoustic source, the known velocity of the acoustic signal in the water, and a velocity model of the formation layers below the sea floor, the depth of the various acoustic reflectors can be determined with relatively good accuracy.
The acoustic energy impinging on the sensors may include both an upward propagating wavefield from reflections occurring beneath the sensors and a downward propagating wavefield from reflections at the surface of the water body. The separation of the wavefields may include estimating fluid particle velocities from pressure measurements in at least a portion of the spectrum of the wavefields. However, in addition to the reflected wavefields, the sensors experience an acoustic wavefield propagating directly from the source (the “direct arrival”). An issue in separating the up-going and down-going wavefields is the proper correction of the direct arrival when estimating fluid particle velocities from pressure measurements.